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If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and SC U, then dim(U) 3. If S is a spanning set for U, then dim(U) 3. If span(S) = U then S linearly independent. If S is a basis for U, then S linearly independent.

If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and SC U, then dim(U) 3. If S is a spanning set for U, then dim(U) 3. If span(S) = U then S linearly independent. If S is a basis for U, then S linearly independent.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”. Fill in the blanks so that the following statements are true. If you believe you don't have enough information to conclude anything for any of the cases, choose the answer "???". Note that there is no intended relationship between the parts. In each case, assume only what the statement says to assume. If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and S C U, then dim(U) 3. If S' is a spanning set for U, then dim(U) 3. If span(S) = U then S If S is a basis for U, then S linearly independent. linearly independent.
Transcribed Image Text:Let U be a subspace of R", and let S = { ū, v, w } be a set of three non-zero vectors in R”. Fill in the blanks so that the following statements are true. If you believe you don't have enough information to conclude anything for any of the cases, choose the answer "???". Note that there is no intended relationship between the parts. In each case, assume only what the statement says to assume. If SCU, then dim(U) > (Enter the largest integer that makes the statement necessarily true.) If S is linearly independent and S C U, then dim(U) 3. If S' is a spanning set for U, then dim(U) 3. If span(S) = U then S If S is a basis for U, then S linearly independent. linearly independent.
Suppose that is a vector of length 2 which is orthogonal to some other vector . Then ū · (2ū + 7v) + ||proj-(2ū) + projū||
Transcribed Image Text:Suppose that is a vector of length 2 which is orthogonal to some other vector . Then ū · (2ū + 7v) + ||proj-(2ū) + projū||
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